— class: inverse background-image: url(“figures/inverse_bg.png”)
.pull-left[ ] .pull-right[ - T cells express Ki67 protein for ~ 4 days after the division. .right[Hogan et. al., PNAS 2015]] - Hard to untangle the origin of Ki67 expression within peripheral naive T cells. Thymic Inheritance or division in periphery?
–
–
\[ \text{Joint Likelihood} \Rightarrow p(y | \hat \theta) = \prod_{i=1}^n \, \text{Normal}(y_i - \text{model}(\theta)_i^\text{pred}, \, \sigma) \]
??? We form a joint likelihood for each model assuming the errors were normally distributed.
–
\[ p(\hat \theta | y) = \frac{p(y | \hat \theta) \times p(\theta_\text{prior})} {p(y)} \]
–
class: center, middle
class: center, middle
–
class: center, middle
Naive T cells of age ‘a’ and Ki67 expression ‘k’ are tracked over time by analytically solving the 3 dimensional PDE,
.shadedbox[ \[ \begin{aligned} \frac{\partial N}{\partial t} + \frac{\partial N}{\partial a} - \beta \, k \, \frac{\partial N}{\partial k}= -(\rho(a) + \delta(a)) \, N(t, a, k) \end{aligned} \]]
class: center, middle
class: center, middle
class: center, middle
Slides created via the R package xaringan.
The chakra comes from remark.js, knitr, and R Markdown.